New Algorithm Enhances Computation of Stabilizer Rényi Entropy in Spin Systems

A new algorithm for calculating stabilizer Rényi entropy in spin systems has been developed by researchers Zejun Liu and Bryan K. Clark. This algorithm, detailed in their paper titled "Non-equilibrium Quantum Monte Carlo Algorithm for Stabilizer Rényi Entropy in Spin Systems," offers an efficient method for computing this measure of quantum magic, which characterizes the classical simulability of quantum systems.

The algorithm leverages quantum Monte Carlo simulations to analyze the path integral of work between two partition function ensembles. It is applicable across all spatial dimensions and temperatures, making it versatile for various quantum systems. The authors demonstrated its effectiveness on one- and two-dimensional transverse field Ising models at both finite and zero temperatures, achieving results that align quantitatively with existing tensor-network based algorithms.

Additionally, the researchers provided an analysis of the computational cost associated with their algorithm, presenting both analytical and numerical evidence that suggests the cost scales polynomially with system size. This finding is significant as it indicates the potential for practical applications in quantum computing and simulations, where efficient algorithms are crucial for handling complex quantum systems.

The full paper can be accessed on arXiv under the identifier arXiv:2405.19577.